Worm Gear Efficiency Calculator — Ratio, Output Torque & Self-Locking Check
Calculate worm gear ratio (single or multi-start), output torque accounting for efficiency losses, and check whether the gear set is self-locking.
Quick Answer
For a 4-start worm driving a 40-tooth worm gear at 30° lead angle, 100 Nm input torque: Ratio = 10:1, Efficiency ≈ 85%, Output Torque ≈ 850 Nm, and Not self-locking (lead angle > friction angle). Use the calculator with your parameters.
How Worm Gear Calculations Work
Worm gears achieve massive reduction in a single stage — but at a cost: efficiency. Here’s the science:
1. Worm Gear Ratio
Ratio = Z_g / Z_w, where Z_g = worm gear teeth, Z_w = number of worm starts (threads). A single-start worm with a 60-tooth gear = 60:1. A 4-start worm with the same gear = 15:1. More starts = lower ratio, higher efficiency, but less self-locking.
2. Efficiency
η = tan(λ) / tan(λ + φ), where λ = worm lead angle, φ = friction angle (arctan of coefficient of friction). This is why efficiency drops as ratio increases — higher ratio means smaller lead angle. Single-start worms can be as low as 35% efficient.
3. Self-Locking Condition
A worm gear is self-locking when λ ≤ φ (lead angle ≤ friction angle). This means you can’t back-drive the gear — the worm holds position even without a brake. Critical for hoists, elevators, and lifts where safety depends on it.
Application Examples
- Elevator and lift hoist mechanisms (self-locking required)
- Conveyor head drives needing high reduction in one stage
- Rotary table indexing for machine tools
- Tuning pegs on string instruments (compact, self-locking)
- Steering gearboxes on heavy vehicles
Common Mistakes
- Assuming all worm gears are self-locking — Multi-start worms (>2 starts) lose self-locking. A 4-start worm at 25° lead angle will absolutely back-drive. Don’t bet safety on it.
- Ignoring efficiency at high ratios — A 60:1 worm set might be only 40% efficient. That means 60% of input power becomes heat. You need cooling or oversized motor.
- Using wrong friction coefficient — Steel worm + bronze gear: μ ≈ 0.04-0.06 (well-lubricated). Steel + cast iron: μ ≈ 0.08-0.10. The difference doubles your efficiency calculation.
- Forgetting break-in wear — New worm sets are 5-8% less efficient. After 50-100 hours of break-in, efficiency improves as surfaces polish. Design for post-break-in performance.
- Not checking thermal capacity — At <50% efficiency, a 10 kW input dumps 5+ kW as heat into the gearbox. Without cooling fins or fan, you'll cook the oil in 30 minutes.
Frequently Asked Questions
How do I know if my worm gear is self-locking?
If the worm lead angle is less than the friction angle, it self-locks. In practice: single-start worms with ratios >30:1 are generally self-locking. Double-start: borderline. Triple-start or higher: not self-locking. Our calculator checks this automatically.
Why is worm gear efficiency so much lower than spur gears?
Spur gears have rolling contact. Worm gears have sliding contact — the worm thread slides across the gear tooth face. Sliding friction generates heat. The efficiency formula tan(λ)/tan(λ+φ) comes directly from this sliding action physics.
What is the maximum single-stage worm gear ratio?
Practical maximum is 100:1. Above that, the lead angle is so small that efficiency drops below 20% and the gear can’t transmit useful power. For higher ratios, use two-stage. See our Gear Ratio Calculator for multi-stage designs.
Can worm gears transmit motion in reverse?
Only if not self-locking and designed for it. Reverse-driving wears the gear quickly because the gear tooth now drives the worm — sliding contact direction reverses. Special “reversing worm” designs exist but are rare.
What oil should I use for worm gears?
ISO VG 460-680 gear oil with EP (extreme pressure) additives for steel-bronze pairs. The thick oil maintains film strength under sliding contact. For food-grade applications, use synthetic PAO oils. Our Hydraulic Pump Calculator covers lubrication system sizing.
How do I calculate output torque correctly?
T_out = T_in × Ratio × η. Don’t forget the efficiency factor! At 40% efficiency and 60:1 ratio, you get 60 × 0.4 = 24× torque multiplication — not 60×. This is the number one reason worm gear drives are undersized.
What materials for worm and gear?
Worm: hardened and ground steel (case-hardened 8620 or through-hardened 4140). Gear: centrifugally cast bronze (C93200 or C95400). The dissimilar metals reduce galling. Cast iron gear is cheaper but only for low-speed, low-load applications.
How does temperature affect worm gear performance?
Rising temperature drops oil viscosity → thinner film → more metal contact → more heat. Thermal runaway. Above 90°C oil temperature, efficiency can drop 15-20%. Active cooling (fan, water jacket) is mandatory above 5 kW continuous.